Problem: Rewrite as a simplified fraction. ${0.1\overline{60} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 160.606...\\ 10x &= 1.606...\end{align*}}$ Subtracting the two equations, we have: ${990x = 159}$ ${x = \dfrac{159}{990}} $ ${x = \dfrac{53}{330}} $